Long distance $c \to u γ$ effects in weak radiative decays of D-mesons

Abstract

We present a detailed analysis of the $D \to V γ$ transitions, using a model which combines heavy quark effective theory and the chiral Lagrangian approach and includes symmetry breaking. We notice that in addition to the previously considered s - channel annihilation and t - channel W - exchange, there is a long distance penguin - like $ c \to u γ$ contribution in the t - channel of Cabibbo - suppressed modes. Its magnitude is determined by the size of symmetry breaking which we calculate with a vector dominance approach. Although smaller in magnitude, the penguin - like contribution would lead to sizeable effects in case of cancellations among the other contributions to the amplitude. Thus, it may invalidate suggested tests for beyond the standard model effects in these decays. We also indicate the range of expectations for the branching ratios of various $D \to V γ$ modes.